Abstract

This paper is on homonymous distributed systems where processes are prone to crash failures and have no initial knowledge of the system membership (“homonymous” means that several processes may have the same identiﬁer). New classes of failure detectors suited to these systems are ﬁrst deﬁned. Among them, the classes HΩ and HΣ are introduced that are the homonymous counterparts of the classes Ω and Σ, respectively. (Recall that the pair hΩ,Σi deﬁnes the weakest failure detector to solve consensus.) Then, the paper shows how HΩ and HΣ can be implemented in homonymous systems without membership knowledge (under different synchrony requirements). Finally, two algorithms are presented that use these failure detectors to solve consensus in homonymous asynchronous systems where there is no initial knowledge of the membership. One algorithm solves consensus with hHΩ, HΣi, while the other uses only HΩ, but needs a majority of correct processes.
Observe that the systems with unique identiﬁers and anonymous systems are extreme cases of homonymous systems
from which follows that all these results also apply to these systems. Interestingly, the new failure detector class HΩ can be implemented with partial synchrony, while the analogous class AΩ deﬁned for anonymous systems can not be implemented(even in synchronous systems). Hence, the paper provides us with the ﬁrst proof showing that consensus can be solved in anonymous systems with only partial synchrony (and a majority of correct processes).